To calculate string $S$-matrix, we mainly use Faddeev-Popov gauge fixing method, as in chapter 6 of Polchinsky's book 《string theory》. But in section 6.2, 'tree level amplitude', I didn't find that it calculates the path integral corresponding to the ghost fields, it only calculates the generating functional corresponding to the matter fields, so i still don't know how to calculate the string path integral to compute tree level amplitude. Can any one elaborate that?
The following is from .section 6.2 in Polchinsky 《String theory》: if you have the book in your hand you can look at it. I think that generating functional is only for ordinary field but does not deal with ghost field. in the next section 6.3 it starts dealing with calculating particular vertex operator expectation value using this generating functional and never compute ghost fields.